Christopher Zoppou | The Australian National University (original) (raw)

Papers by Christopher Zoppou

Space-Time Conservation Method Applied to Saint Venant Equations

Journal of Hydraulic Engineering, Aug 1, 1999

The authors have adapted the numerical scheme developed by Chang (1995) for the solution of the s... more The authors have adapted the numerical scheme developed by Chang (1995) for the solution of the shallow water wave equations. The explicit scheme is conservative in both space and time. To demonstrate the accuracy of the scheme, the authors use the space-time conservation scheme to solve the instantaneous breach of a dam in a horizontal frictionless channel. This problem has an analytical solution, which is given by Stoker (1957). In their paper, the results of their model is compared with the results produced from the Lax- ...

The Validity of Backwater Models for Flood Routing Applications

7th Australasian Conference on Hydraulics and Fluid Mechanics 1980: Preprints of Papers, 1980

Abstract: Backwater profile computer packages such as the US Army Corps of Engineers&#x27... more Abstract: Backwater profile computer packages such as the US Army Corps of Engineers' HEC-2 are being widely used in flood studies - in particular for simulating high water levels along river reaches. These "known-discharge" models consider the inflow hydrograph as a sequence of discrete discharge steps. Flows along the channel are frozen during each time interval and the water surface profile is determined by a backwater model. The equations used in these models can be considered as simplified versions of the complete one-dimensional Saint Venant ...

Decision support system for assessing integrated Urban water systems

10th World Water Congress: Water, the Worlds Most Important Resource, 2000

A computer-based tool that has been developed to aid in the analysis of alternatives to tradition... more A computer-based tool that has been developed to aid in the analysis of alternatives to traditional methods of providing water services in urban areas is described. The model is called TAWS and has been implemented as a decision support system (DSS). The modelling approach adopted integrates water supply, wastewater and stormwater services into a single framework. Alternative water systems are evaluated using infrastructure life cycle cost subject to water quality, hydrologic and hydraulic constraints. The TAWS DSS ...

Closure to “Catastrophic Collapse of Water Supply Reservoirs in Urban Areas” by Christopher Zoppou and Stephen Roberts

Journal of Hydraulic Engineering, Mar 1, 2001

The authors discuss in their paper two points related to the method mentioned in the title:(1) a ... more The authors discuss in their paper two points related to the method mentioned in the title:(1) a modification they introduce in order to take into account the longitudinal hydraulic pressure gradient term; and (2) volume conservation (or, rather, deficiency of volume conservation) as observed in various ''commonly used schemes.''Concerning the first point, the discusser would like to limit his discussion to two general remarks:

Discussion of "Uncertainty Analysis of Dredge Production with Correlation

Journal of Waterway Port Coastal and Ocean Engineering-asce, Mar 1, 1996

Page 2.32, 2nd last paragraph replace "second-accurate" with second-order accurate".

Water Resources Research, Nov 1, 1994

Environmental Modelling and Software, Apr 1, 2001

This paper reviews models for simulating storm water quantity and quality in an urban environment... more This paper reviews models for simulating storm water quantity and quality in an urban environment. This has been achieved by examining a number of storm water models in current use. The important features of twelve models, which represent a wide range of capabilities and spatial and temporal resolution have been described. Specific topics covered are: identifying important urban water quality parameters; the classification of modelling approaches; modelling approaches used to estimate water quantity and quality. These include statistical, empirical, hydraulic and hydrological models. Water resources management and planning tools, that are included in some urban storm water models, such as economic analysis, optimisation and risk analysis are also discussed. Features of twelve storm water models have been summarised. These models have been chosen because they demonstrate how components that are important in managing urban storm water have been incorporated in a modelling framework. These models have been categorised in terms of their functionality, accessibility, water quantity and quality components included in the model and their temporal and spatial scale. The information in this paper provides planners and managers with an overview of modelling approaches that have been used to simulate storm water quantity and quality. In particular, it provides managers with an appreciation of the limitations and assumptions made in various modelling approaches. This review will also benefit modellers by providing a comprehensive summary of approaches and capabilities of a number of storm water models in current use. Potential urban storm water research opportunities have also been identified.

Conservative Semi-Lagrangian Algorithm for Pollutant Transport in Rivers. Discussion and Closure

Journal of Environmental Engineering, Sep 1, 2000

The Mamala Bay Study (MBS) was the initial outgrowth of a pair of legal actions brought against t... more The Mamala Bay Study (MBS) was the initial outgrowth of a pair of legal actions brought against the City and County of Honolulu (CCH) by two environmental groups and funded by $9,000,000 of CCH monies. Of concern were two large primary-treated rather than secondary-treated wastewater effluents. One involved 3 m3/s flowing into 72 m of water off Sand Island; the other involved 1 m3/s issuing into a 61 m ocean depth off Honouliuli (Grace 1978). This whole affair was a very emotionally charged and contentious issue in ...

Rapidly-varying free surface flows that arise, for example, from; rapid reservoir releases, dambr... more Rapidly-varying free surface flows that arise, for example, from; rapid reservoir releases, dambreaks, mud slides, tidal bores, storm surges, tsunamis and flows over variable topography, are characterized by abrupt changes in the water surface. These changes produce vertical acceleration of the fluid particles. These vertical accelerations manifest as a series of oscillating waves, called dispersive waves, which follow abrupt changes in the water surface. These dispersive waves can have a significant influence on the water depth which impacts on the area inundated by these flows. viii cluding dispersive terms when simulating rapidly-varying flows. These examples demonstrate the accuracy, robustness and versatility of the Serre equations in modelling dispersive waves. The computer programs developed are simple to implement, efficient and stable for a range of problems, including rapidly-varying free surface flows.

Australian & New Zealand industrial and applied mathematics journal, Jun 5, 2016

The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These ... more The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These include mixed spatial and temporal derivative flux terms which are difficult to handle numerically. These terms can be replaced by an alternative combination of equivalent temporal and spatial terms, so that the Serre equations can be written in conservation law form. The water depth and new conserved quantities are evolved using a second-order finite-volume scheme. The remaining primitive variable, the depthaveraged horizontal velocity, is obtained by solving a second-order elliptic equation using simple finite differences. Using an analytical solution and simulating the dambreak problem, the proposed scheme is shown to be accurate, simple to implement and stable for a range of problems, including flows with steep gradients. It is only slightly more computationally expensive than solving the shallow water wave equations.

arXiv (Cornell University), Jun 27, 2017

We use numerical methods to study the behaviour of the Serre equations in the presence of steep g... more We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial condition problems that are a smooth approximation to the initial conditions of the dam-break problem. This class of initial condition problems allow us to observe the behaviour of the Serre equations with varying steepness of the initial conditions. The numerical solutions of the Serre equations are justified by demonstrating that as the resolution increases they converge to a solution with little error in conservation of mass, momentum and energy independent of the numerical method. We observe four different structures of the converged numerical solutions depending on the steepness of the initial conditions. Two of these structures were observed in the literature, with the other two not being commonly found in the literature. The numerical solutions are then used to assess how well the analytical solution of the shallow water wave equations captures the mean behaviour of the solution of the Serre equations for the dam-break problem. Lastly the numerical solutions are used to evaluate the usefulness of asymptotic results in the literature to approximate the depth and location of the front of an undular bore.

Application of Simulated Annealing for Integrated Urban Water Systems: Infrastructure, Treatment and Re-Use Optimization

Escalating costs in providing water supply, waste water and storm water infrastructure and commun... more Escalating costs in providing water supply, waste water and storm water infrastructure and community concerns over the environmental impact of water harvesting and effluent disposal, have focused attention on providing these services in an economically efficient and ecologically sustainable way. To exploit emerging technologies and re-use options it is essential that these are assesed in an integrated water system which includes water supply, waste and storm water treatment and disposal infrastructure. Optimisation provides an ...

Discussion of Unsteady Finite-Analytic Method for Solute Transport in Ground-Water Flow by Whey-Fone Tsai and Ching-Jen Chen

Journal of Engineering Mechanics-asce, 1996

This paper examines the quasi-characteristic method for the solution of the Saint Venant equation... more This paper examines the quasi-characteristic method for the solution of the Saint Venant equations governing the motion of flows, waves and floods in rivers and channels. The apparently new approach combines the more desirable features of traditional numerical methods, but does riot seem to suffer from their disadvantages. It is explicit, efficient, accurate and simple to implement. However, it is shown that the existing formulation has demanding stability criteria if friction, inflow and/or a non-prismoidal channel are considered. A simple modification of the method yields a scheme which has finite stability criteria but which are not particularly restrictive. The performance of the method is compared with existing numerical methods in the solution of a particular problem.

Closure to “Reverse Routing of Flood Hydrographs Using Level Pool Routing” by Christopher Zoppou

Journal of Hydrologic Engineering, 2001

Spatial and Temporal Rainfall Interpolation Using Finite Element Thin Plate Splines

Water 99: Joint Congress; 25th Hydrology & Water Resources Symposium, 2nd International Conference on Water Resources & Environment Research; Handbook and Proceedings, 1999

Solving the fully nonlinear weakly dispersive Serre equations for flows over dry beds

International Journal for Numerical Methods in Fluids, Jul 26, 2020

We describe a numerical method for solving the Serre equations that can simulate flows over dry b... more We describe a numerical method for solving the Serre equations that can simulate flows over dry bathymetry. The method solves the Serre equations in conservation law form with a finite volume method. A finite element method is used to solve the auxiliary elliptic equation for the depth‐averaged horizontal velocity. The numerical method is validated against the lake at rest analytic solution, demonstrating that it is well‐balanced. Since there are currently no known nonstationary analytical solutions to the Serre equation that involve bathymetry, a nonstationary forced solution, involving bathymetry was developed. The method was further validated and its convergence rate established using the developed nonstationary forced solution containing the wetting and drying of bathymetry. Finally, the method is also validated against experimental results for the run‐up of a solitary wave on a sloped beach. The finite‐volume finite‐element approach to solving the Serre equation was found to be accurate and robust.

Reverse Routing of Flood Hydrographs Using Level Pool Routing

Journal of Hydrologic Engineering, Jun 1, 2001

In level pool routing, which is the simplest hydrological routing method, the downstream discharg... more In level pool routing, which is the simplest hydrological routing method, the downstream discharge may be expressed explicitly in terms of the inflow and the channel or reservoir characteristics. The level pool routing equation can also be used to estimate the inflow hydrograph given the outflow hydrograph and the water level in the reservoir. Unfortunately, use of the traditional level pool routing method, which is based on the implicit finite difference scheme, for reverse routing has been unsuccessful, despite the simplicity of the ...

Spatial and temporal rainfall interpolation using generalized additive

Space-Time Conservation Method Applied to Saint Venant Equations

Journal of Hydraulic Engineering, Aug 1, 1999

The authors have adapted the numerical scheme developed by Chang (1995) for the solution of the s... more The authors have adapted the numerical scheme developed by Chang (1995) for the solution of the shallow water wave equations. The explicit scheme is conservative in both space and time. To demonstrate the accuracy of the scheme, the authors use the space-time conservation scheme to solve the instantaneous breach of a dam in a horizontal frictionless channel. This problem has an analytical solution, which is given by Stoker (1957). In their paper, the results of their model is compared with the results produced from the Lax- ...

The Validity of Backwater Models for Flood Routing Applications

7th Australasian Conference on Hydraulics and Fluid Mechanics 1980: Preprints of Papers, 1980

Abstract: Backwater profile computer packages such as the US Army Corps of Engineers&#x27... more Abstract: Backwater profile computer packages such as the US Army Corps of Engineers' HEC-2 are being widely used in flood studies - in particular for simulating high water levels along river reaches. These "known-discharge" models consider the inflow hydrograph as a sequence of discrete discharge steps. Flows along the channel are frozen during each time interval and the water surface profile is determined by a backwater model. The equations used in these models can be considered as simplified versions of the complete one-dimensional Saint Venant ...

Decision support system for assessing integrated Urban water systems

10th World Water Congress: Water, the Worlds Most Important Resource, 2000

A computer-based tool that has been developed to aid in the analysis of alternatives to tradition... more A computer-based tool that has been developed to aid in the analysis of alternatives to traditional methods of providing water services in urban areas is described. The model is called TAWS and has been implemented as a decision support system (DSS). The modelling approach adopted integrates water supply, wastewater and stormwater services into a single framework. Alternative water systems are evaluated using infrastructure life cycle cost subject to water quality, hydrologic and hydraulic constraints. The TAWS DSS ...

Closure to “Catastrophic Collapse of Water Supply Reservoirs in Urban Areas” by Christopher Zoppou and Stephen Roberts

Journal of Hydraulic Engineering, Mar 1, 2001

The authors discuss in their paper two points related to the method mentioned in the title:(1) a ... more The authors discuss in their paper two points related to the method mentioned in the title:(1) a modification they introduce in order to take into account the longitudinal hydraulic pressure gradient term; and (2) volume conservation (or, rather, deficiency of volume conservation) as observed in various ''commonly used schemes.''Concerning the first point, the discusser would like to limit his discussion to two general remarks:

Discussion of "Uncertainty Analysis of Dredge Production with Correlation

Journal of Waterway Port Coastal and Ocean Engineering-asce, Mar 1, 1996

Page 2.32, 2nd last paragraph replace "second-accurate" with second-order accurate".

Water Resources Research, Nov 1, 1994

Environmental Modelling and Software, Apr 1, 2001

This paper reviews models for simulating storm water quantity and quality in an urban environment... more This paper reviews models for simulating storm water quantity and quality in an urban environment. This has been achieved by examining a number of storm water models in current use. The important features of twelve models, which represent a wide range of capabilities and spatial and temporal resolution have been described. Specific topics covered are: identifying important urban water quality parameters; the classification of modelling approaches; modelling approaches used to estimate water quantity and quality. These include statistical, empirical, hydraulic and hydrological models. Water resources management and planning tools, that are included in some urban storm water models, such as economic analysis, optimisation and risk analysis are also discussed. Features of twelve storm water models have been summarised. These models have been chosen because they demonstrate how components that are important in managing urban storm water have been incorporated in a modelling framework. These models have been categorised in terms of their functionality, accessibility, water quantity and quality components included in the model and their temporal and spatial scale. The information in this paper provides planners and managers with an overview of modelling approaches that have been used to simulate storm water quantity and quality. In particular, it provides managers with an appreciation of the limitations and assumptions made in various modelling approaches. This review will also benefit modellers by providing a comprehensive summary of approaches and capabilities of a number of storm water models in current use. Potential urban storm water research opportunities have also been identified.

Conservative Semi-Lagrangian Algorithm for Pollutant Transport in Rivers. Discussion and Closure

Journal of Environmental Engineering, Sep 1, 2000

The Mamala Bay Study (MBS) was the initial outgrowth of a pair of legal actions brought against t... more The Mamala Bay Study (MBS) was the initial outgrowth of a pair of legal actions brought against the City and County of Honolulu (CCH) by two environmental groups and funded by $9,000,000 of CCH monies. Of concern were two large primary-treated rather than secondary-treated wastewater effluents. One involved 3 m3/s flowing into 72 m of water off Sand Island; the other involved 1 m3/s issuing into a 61 m ocean depth off Honouliuli (Grace 1978). This whole affair was a very emotionally charged and contentious issue in ...

Rapidly-varying free surface flows that arise, for example, from; rapid reservoir releases, dambr... more Rapidly-varying free surface flows that arise, for example, from; rapid reservoir releases, dambreaks, mud slides, tidal bores, storm surges, tsunamis and flows over variable topography, are characterized by abrupt changes in the water surface. These changes produce vertical acceleration of the fluid particles. These vertical accelerations manifest as a series of oscillating waves, called dispersive waves, which follow abrupt changes in the water surface. These dispersive waves can have a significant influence on the water depth which impacts on the area inundated by these flows. viii cluding dispersive terms when simulating rapidly-varying flows. These examples demonstrate the accuracy, robustness and versatility of the Serre equations in modelling dispersive waves. The computer programs developed are simple to implement, efficient and stable for a range of problems, including rapidly-varying free surface flows.

Australian & New Zealand industrial and applied mathematics journal, Jun 5, 2016

The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These ... more The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These include mixed spatial and temporal derivative flux terms which are difficult to handle numerically. These terms can be replaced by an alternative combination of equivalent temporal and spatial terms, so that the Serre equations can be written in conservation law form. The water depth and new conserved quantities are evolved using a second-order finite-volume scheme. The remaining primitive variable, the depthaveraged horizontal velocity, is obtained by solving a second-order elliptic equation using simple finite differences. Using an analytical solution and simulating the dambreak problem, the proposed scheme is shown to be accurate, simple to implement and stable for a range of problems, including flows with steep gradients. It is only slightly more computationally expensive than solving the shallow water wave equations.

arXiv (Cornell University), Jun 27, 2017

We use numerical methods to study the behaviour of the Serre equations in the presence of steep g... more We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial condition problems that are a smooth approximation to the initial conditions of the dam-break problem. This class of initial condition problems allow us to observe the behaviour of the Serre equations with varying steepness of the initial conditions. The numerical solutions of the Serre equations are justified by demonstrating that as the resolution increases they converge to a solution with little error in conservation of mass, momentum and energy independent of the numerical method. We observe four different structures of the converged numerical solutions depending on the steepness of the initial conditions. Two of these structures were observed in the literature, with the other two not being commonly found in the literature. The numerical solutions are then used to assess how well the analytical solution of the shallow water wave equations captures the mean behaviour of the solution of the Serre equations for the dam-break problem. Lastly the numerical solutions are used to evaluate the usefulness of asymptotic results in the literature to approximate the depth and location of the front of an undular bore.

Application of Simulated Annealing for Integrated Urban Water Systems: Infrastructure, Treatment and Re-Use Optimization

Escalating costs in providing water supply, waste water and storm water infrastructure and commun... more Escalating costs in providing water supply, waste water and storm water infrastructure and community concerns over the environmental impact of water harvesting and effluent disposal, have focused attention on providing these services in an economically efficient and ecologically sustainable way. To exploit emerging technologies and re-use options it is essential that these are assesed in an integrated water system which includes water supply, waste and storm water treatment and disposal infrastructure. Optimisation provides an ...

Discussion of Unsteady Finite-Analytic Method for Solute Transport in Ground-Water Flow by Whey-Fone Tsai and Ching-Jen Chen

Journal of Engineering Mechanics-asce, 1996

This paper examines the quasi-characteristic method for the solution of the Saint Venant equation... more This paper examines the quasi-characteristic method for the solution of the Saint Venant equations governing the motion of flows, waves and floods in rivers and channels. The apparently new approach combines the more desirable features of traditional numerical methods, but does riot seem to suffer from their disadvantages. It is explicit, efficient, accurate and simple to implement. However, it is shown that the existing formulation has demanding stability criteria if friction, inflow and/or a non-prismoidal channel are considered. A simple modification of the method yields a scheme which has finite stability criteria but which are not particularly restrictive. The performance of the method is compared with existing numerical methods in the solution of a particular problem.

Closure to “Reverse Routing of Flood Hydrographs Using Level Pool Routing” by Christopher Zoppou

Journal of Hydrologic Engineering, 2001

Spatial and Temporal Rainfall Interpolation Using Finite Element Thin Plate Splines

Water 99: Joint Congress; 25th Hydrology & Water Resources Symposium, 2nd International Conference on Water Resources & Environment Research; Handbook and Proceedings, 1999

Solving the fully nonlinear weakly dispersive Serre equations for flows over dry beds

International Journal for Numerical Methods in Fluids, Jul 26, 2020

We describe a numerical method for solving the Serre equations that can simulate flows over dry b... more We describe a numerical method for solving the Serre equations that can simulate flows over dry bathymetry. The method solves the Serre equations in conservation law form with a finite volume method. A finite element method is used to solve the auxiliary elliptic equation for the depth‐averaged horizontal velocity. The numerical method is validated against the lake at rest analytic solution, demonstrating that it is well‐balanced. Since there are currently no known nonstationary analytical solutions to the Serre equation that involve bathymetry, a nonstationary forced solution, involving bathymetry was developed. The method was further validated and its convergence rate established using the developed nonstationary forced solution containing the wetting and drying of bathymetry. Finally, the method is also validated against experimental results for the run‐up of a solitary wave on a sloped beach. The finite‐volume finite‐element approach to solving the Serre equation was found to be accurate and robust.

Reverse Routing of Flood Hydrographs Using Level Pool Routing

Journal of Hydrologic Engineering, Jun 1, 2001

In level pool routing, which is the simplest hydrological routing method, the downstream discharg... more In level pool routing, which is the simplest hydrological routing method, the downstream discharge may be expressed explicitly in terms of the inflow and the channel or reservoir characteristics. The level pool routing equation can also be used to estimate the inflow hydrograph given the outflow hydrograph and the water level in the reservoir. Unfortunately, use of the traditional level pool routing method, which is based on the implicit finite difference scheme, for reverse routing has been unsuccessful, despite the simplicity of the ...

Spatial and temporal rainfall interpolation using generalized additive